Atom-motion-induced localization and meson confinement in Rydberg-atom ladders

Rydberg-atom arrays provide a programmable platform for quantum simulation of Ising models, where confinement of domain-wall excitations can famously arise from the addition of a longitudinal field. These confined excitations, often referred to as mesons by analogy with particle physics, lead to reduced entanglement growth and suppressed correlation spreading across the system. Similar signatures, however, can also result from disorder-induced localization in noisy intermediate-scale quantum devices. Here, we investigate the crossover between confinement-driven and disorder-driven dynamics in Ising chains and ladders realized on a remotely accessible Rydberg-atom array platform. We chart out all features that differentiate these two distinct phenomena, and introduce an order-parameter-like quantity for the crossover based on the meson mass spectroscopy. Furthermore, we develop a semi-analytic theory for the relevant meson excitations on ladders for both weakly and strongly interacting transverse field Ising chains (TFICs), identifying two distinct meson types, and benchmark its predictions using exact diagonalization and matrix product state simulations. By experimentally probing one of these meson types in different interaction strengths, our work highlights that the confinement can dominate over the atom-motion-induced disorder in the TFIC regime of Rydberg atom arrays solely due to lattice dimensionality and many-body interactions.